Let $$xi(1$$≤i≤$$10)$$ be ten observations of a random variable X. If ∑$$i=110$$ xi−$$p=3$$ and ∑$$i=110$$ xi−$$p2=9$$, $$where0$$≠p∈R, then the standard deviation of these observations is

Question

Let $$xi(1$$≤i≤$$10)$$ be ten observations of a random variable  X. If ∑$$i=110$$ xi−$$p=3$$ and ∑$$i=110$$ xi−$$p2=9$$, $$where0$$≠p∈R, then the standard deviation of these observations is

Infinity Learn · Accepted Answer

Let σX be the standard deviation. Then,σ$$X2=110$$Σxi−$$p2$$−$$110$$Σxi−$$p2=910$$−$$3102=81100$$⇒ σ$$x=910It$$ follows from the above discussion that in case of individual observations, $$variance/$$ standard deviation may be computed by applying any of the above three formulas. In order to calculate the variance when deviations are taken from the actual mean, we may use the following algorithm.

Let $x_{i} (1 \leq i \leq 10)$ be ten observations of a random variable $X. If \sum_{i = 1}^{10} (x_{i} - p) = 3 and \sum_{i = 1}^{10} {(x_{i} - p)}^{2} = 9$ , where
$0 \neq p \in R,$ then the standard deviation of these observations is

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Let xi(1≤i≤10) be ten observations of a random variable X. If ∑i=110 xi−p=3 and ∑i=110 xi−p2=9, where0≠p∈R, then the standard deviation of these observations is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

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Let $x_{i} (1 \leq i \leq 10)$ be ten observations of a random variable $X. If \sum_{i = 1}^{10} (x_{i} - p) = 3 and \sum_{i = 1}^{10} {(x_{i} - p)}^{2} = 9$ , where
$0 \neq p \in R,$ then the standard deviation of these observations is